I can do the things that you have there, you can take a look at my site here:
http://jonhmchan.com/If you need resources as to how to learn flash, there's a lot of material on the Adobe site. That's how I learned: go to the 'How To' section on Adobe TV online under 'Channels', and click on the 'Flash' section. You can also search 'Learn Flash Professional CS4 - Getting Started'.
EDIT:
Here's the first video
In addition, if your company is only trying to make flash banners and little snippets, you might be better off using a program like
Swish and integrate with HTML - it's sort of a simplified version of Flash that is much more accessible to beginners without the big cloud of learning Actionscript from scratch.
But when it comes to learning how to do news/shows sections (I'm not entirely sure what you mean, the link you gave doesn't work) you should probably get your hands on PHP/MySQL. These are languages that help you store and work with data without having to make the big hassle through big blocks of code to make small updates. But if you're doing little things, then you might just stick with what you have.
What sort of experience does your company have? What languages do they know already?